Abstract
The compression of relativistic electron beams resulting from partial space charge neutralization by thermal ions is simulated to obtain self-consistent solutions. The numerical modeling is based on a finite difference approach, using under-relaxation to assure convergence in solving this nonlinear problem. The results show a nonuniform fraction of neutralization, increasing as a function of radius. Neutralization on axis is higher for colder compensating ions and for lower electron energy. In general, the temperature of the ions turns out to be higher than that of the electrons. With respect to the non-neutralized, not-thermally-dispersed beam, higher compression factors result at higher beam energies. The analytic solutions, known as the Bennett pinch, are well matched at corresponding settings of the parameters.
Highlights
Electron beams without external focusing are found in several applications: electron beam welding, x-ray tomography scanners, and special kinds of electron beam ion sources and traps (EBIS and EBIT)
The propagation of these beams is determined by their self-electric and selfmagnetic fields, causing beam spreading by space charge, its reduction by ion neutralization, and additional focusing by pinching at relativistic energies
For the modeling of the behavior of thermal electrons and thermal ions, selfconsistent solutions are required for the radial distribution functions
Summary
Electron beams without external focusing are found in several applications: electron beam welding, x-ray tomography scanners, and special kinds of electron beam ion sources and traps (EBIS and EBIT). As early as 1934, Bennett [1] gave the classical treatment for the neutralization of a relativistic electron beam by ions, with transverse Maxwellian distribution of velocities for both kinds of particles. He found particular solutions for the radial variation of charges, based on a constant (as a function of radius) degree of neutralization f. In this paper we present self-consistent solutions that are useful in the area of EBIS and EBIT devices, especially for those working without magnetic field [9,10] These solutions will be used in a forthcoming paper to investigate the matching conditions for the beam entering into the pinched ion trap region
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